MTH212 Tma Solutions
1. Linear transformations are also called vector space __________________
Isomorphism
Inverse
—>> homomorphisms.
Dimension
2. The rank of T is defined to be the _______________________of R(T), the range space of T.
projection
Kernel
function
—>> dimension
3. There are two sets which are associated with any linear transformation, T. These are the range and the ___________________of T
Projection
—>> Kernel
Function
Inverse
4. If T is an isomorphism between U and V then \(T^{-1}\) is an isomorphism between________________________
—>> \(V and U\)
\(U and T^{-1}\)
\(V^{-1} and U\)
\(V and T^{-1}\)
5. Let T:U→V be a linear transformation; If T is injective, we also say T is ______________________
Onto
Surjective
one-zero
—>> one-one
6. The __________________operator is both one-one and onto
Inverse
—>> Identity
Dimension
Range
7. Let U and V be vector spaces over a field F, and let \(T:U \rightarrow V\) be a one-one and onto linear transformation. The T is called an
